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Weather response to management of a large wind turbine array

Daniel B. Barrie1 & Daniel B. Kirk-Davidoff1

1Department of Atmospheric and Oceanic Science, University of Maryland, College Park, MD, US

Summary: Varying the effective roughness of a large wind farm represented in a General Circulation

Model caused changes in downstream weather phenomena.

Electrical generation by wind turbines is increasing rapidly, and has been

projected to satisfy 15% of world electric demand by 20301. To achieve such

growth, wind turbines would be installed over a broad geographic area. Extensive

wind farms would alter surface roughness and would have a significant impact on

the atmospheric circulation2. This impact depends on both the spatial extent and the

effective additional surface roughness caused by the turbines.  The magnitude of the

additional roughness could be changed deliberately by adjustment of the attitude of

the turbine blades with respect to the wind. Using a General Circulation Model

(GCM), we represent a continent-scale wind farm as a distributed array of surface

roughness elements. Here we show that initial disturbances caused by a step change

in surface roughness grow within four days such that the perturbed and

unperturbed flows are different at synoptic scales. The growth rate of the induced

perturbations is largest in regions of high atmospheric instability. For a roughness

change imposed over North America, the induced perturbations become large over

the North Atlantic, where they involve substantial changes in the track and

development of cyclones.

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The development of numerical weather prediction (NWP) by John von Neumann

and Jule Charney was motivated in part from a desire to influence weather at a distance.3

However, von Neumann recognized that the practical means to exert control on large-

scale weather did not yet exist.3 While NWP was being developed, Irving Langmuir and

Vincent Schaefer’s work on cloud seeding provided an early method for manipulating

precipitating systems.4,5 Langmuir suggested that cloud seeding could be used to suppress

hurricanes by altering early convective growth in tropical disturbances.5 More recent

analysis of the failure of early attempts such as Proejct Stormfury to influence the

evolution of hurricanes has shown that the growth and development of perturbations

depends at least as much on the state of the atmosphere at the time of perturbation than

on the shape of the perturbation itself.6

The chaotic growth of small initial perturbations in the atmosphere7 has both

positive and negative implications for weather modification strategies. A small

perturbation in the atmosphere may eventually become large enough to have detectable

consequences for weather. However, chaos limits weather predictability to a few weeks,

since the various atmospheric states consistent with observational uncertainty diverge

completely from one another over that time. Thus deliberate synoptic scale weather

modification requires that initial perturbation be larger than the observational uncertainty

and that the perturbations we are capable of inducing project onto atmospheric modes

with the potential to grow in a desired direction. Hoffman proposed a program of global

weather modification in which global weather would be optimized by systematic

adjustment of all human controlled phenomena that could influence the atmosphere’s

flow.8 Hoffman demonstrated in a model that hurricanes could be steered by creating an

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ideal initial perturbation in the temperature field.9 However, this task required

impractically large energy inputs.

Motivated by our previous work, which showed significant mean changes in

climate due to large-scale wind farms2, we now examine the evolution of perturbations

caused by changes in a fixed array of wind turbines within a synoptic forecast period. The

continental scale of this wind farm is consonant with that of growing atmospheric modes,

and the amplitude of the roughness forcing rises above [typical background observational

uncertainty of ?? m/s in the mean wind???]. Although synoptic-scale perturbations grow

slowly relative to convective scale perturbations7, they saturate at higher amplitudes than

convective modes8, suggesting that weather modification may be possible by taking

advantage of the short-term predictability of mid-latitude instabilities. While large-scale

wind turbine installations like those discussed in this paper do not yet exist, no known

resource limitations would prevent their construction in the near future.

The worldwide wind energy potential has been assessed at 72 Terawatts (TW)9.

Total worldwide electric power consumption is projected to nearly double from 1.9 to 3.5

TW between 2004 and 203010. A large contribution from wind energy is typically

proposed when modeling the power supply system under carbon constraints1,11.

Continued rapid growth of the United States wind industry will result in substantial

development of its wind resource. The central United States will be a focal point of this

development because it hosts the largest contiguous wind resource of any on-shore region

in the United States12. Turbine installation costs are lower there than in any other region

of the United States13. In addition, wind farm developers are willing to pay leasing fees to

farmers for the use of their land to build wind farms, which is a substantial source of

supplemental income14.

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Individual wind turbines affect local momentum transports through the creation of a

cross-blade pressure gradient and turbulent wakes15. The aggregate impact of an array of

wind turbines can be parameterized by a single roughness length16. This is the approach

we have taken using the National Center for Atmospheric Research Community

Atmosphere Model 3.0 (CAM 3.0)17.

Wind farm specification in the model. CAM 3.0 describes land surface

characteristics using the spatial and temporal distribution of 16 Plant Functional Types

(PFTs) across the land surface. Each land grid point can support four unique PFTs, with

coverage adding up to 100% over each grid point18. We have converted an unused PFT

into a wind farm subtype, with a “canopy” height of 156 meters, a ratio of roughness

length to canopy height of .0215, and a displacement height of zero meters. The wind

farm PFT is set to occupy 25% of the surface area within the wind farm region.

The model was run with fixed sea surface temperatures at T42 resolution for six

years with the wind farm present. The wind farm occupies 23% of the North American

land area and is positioned in the central United States. We used typical values of turbine

spacing (.59 km2 per turbine), wind farm capacity factors (35%), and turbine ratings (1

MW) to derive a total expected power output of 3.31 TW from our wind farm. Using 12-

hourly wind stress and wind velocity data, we calculated an average dissipation rate

of .87 TW over the entire model run. This estimate represents a lower bound of power

output in part because it ignores the possibility of correlation between wind stress and

wind at higher frequencies. This suggests that our estimate of surface roughness is

conservative for a wind farm of the envisioned horizontal scale. Seventy-two case studies

were created by running the model in branch mode using the monthly restart files created

during the six years of the control run. Each of the branch runs lasted for one month. For

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these case studies, the wind farm PFT roughness was reduced by 83% to simulate the

minimal drag of a turbine profile, where the face of the turbine is turned so that it is

orthogonal to the wind direction. The branch runs simulate the effect of a sudden, large

reduction in surface roughness on the atmosphere.

Figure 1 shows the mean difference between the case runs and model climatology

in the lower tropospheric eastward wind field. There is an extended downstream region of

significant atmospheric modification that highlights the area where impacts are focused.

The rectangular outline in the figure demonstrates the placement of the wind farm. The

structure of the anomaly is similar to that found in a previous 20 year model run with and

without wind farm forcing, and arises from the dynamical adjustment of the atmosphere

to the surface roughness anomaly2.

During the first few days following the decrease in magnitude of the surface

roughness perturbation in each case, we observe highly localized wind and temperature

anomalies that are contained primarily within the wind farm and depend strongly on the

overlying meteorological conditions. Over the following days, the impacts move

downstream and eventually reach the North Atlantic. There the anomalies grow, and their

magnitudes exceed the magnitude of the response at the wind farm. This is shown in

figure 2a, a Hovmoller plot of the standard deviation over the 72 case studies. The 788-

millibar zonal wind is depicted in the plot and was averaged over the band from 54 to

66°N. The horizontal axis is longitude and the vertical axis is time. Figures 2b and 2c

show time slices of the Hovmoller plot, illustrating the downstream development of the

anomaly patterns.

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The contours in latitude and time in Figure 2a show that the anomalies have a

typical group velocity of 6.4 m/s with an exponential growth rate of 0.30/day. When the

wind farm is first turned off, the largest anomalies are located at the wind farm site. After

four days have passed, the effect of the wind farm is most prominent in the North

Atlantic, and reaches the North Pacific after one week. The anomalies grow faster within

the Atlantic and Pacific storm tracks than over land. After two weeks have elapsed, the

perturbed run has largely diverged from the original run, obscuring the structure of the

wind farm effects, although the largest anomalies are still found over the northern ocean

basins.

Empirical orthogonal function (EOF) analysis was performed on each day post-

disturbance, with case number as the primary dimension. At day five, the dominant EOF

components display a wave-like structure located in the central North Atlantic (Figure 3),

with the primary component accounting for 10.5% of total variability. The first two EOF

components are approximately in quadrature, and depict growing baroclinic modes.

Although the magnitude of the first EOF component is small, the pattern is striking. A

visual inspection of the day five surface zonal wind anomalies over all of the case studies

reveals a number of instances where a southwest to northeast aligned wave train occurs.

Wave amplitude, wavelength, and channel width vary greatly across all of the cases, but

each is confined to the central North Atlantic.

The case studies were also examined to find particularly large meteorological

changes. In one instance, cloudiness was modified by up to 80% over the British Isles

and Ireland four days after the surface roughness change was triggered in the model. This

is shown in figure 4, which plots integrated mid-level cloud cover given as a percentage.

In figure 4a, we see large anomalies in cloud cover. There is a significant difference

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between cloud cover when the farm is turned on (figure 4b), and when the farm is turned

off (figure 4c). This particular result is unusual in that the effect is far removed from the

region where large anomalies are typically observed four days after the roughness

change.

The study presented here depicts a strong downstream impact caused by a large

surface roughness perturbation in a GCM. The active control of turbine orientation would

enable manipulation of the effective surface roughness of a wind farm. We have modeled

this as a time-dependent change in surface roughness. Atmospheric anomalies initially

develop at the wind farm site due to a slowing of the obstructed wind. The anomalies

propagate downstream as a variety of baroclinic and barotropic modes, and grow quickly

when they reach the North Atlantic. These responses occur within a short forecast

timeframe, which suggests that predictable influences on weather may be possible. This

study utilized an array of highly variable initial conditions to initialize the model.

Ongoing work will catalog the initial meteorological conditions necessary to generate

predictable and controlled downstream effects caused by wind farms. We will perform an

ensemble of studies with initial conditions chosen for both the wind farm and the wind

farm absent cases so that the ensemble members project strongly onto the fastest modes

of error growth. This will illustrate the statistical significance and regularity of

downstream changes in the atmosphere.

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12. Elliott, D., Holladay, C.G., Barchet, W.R., Foote, H.P., Sandusky, W.F. Wind energy

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Acknowledgements : We thank Eugenia Kalnay for her comments and suggestions. We acknowledge

Juliana Rew and Samuel Levis, at the National Center for Atmospheric Research (NCAR), for their

assistance. This work was made possible by NSF grant #ATM, and a donation of modelling time by

NCAR.

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[Figure 1] 867 millibar zonal wind anomaly. The mean difference in the

eastward wind in the lower troposphere between the control and perturbed model

runs highlights extended downstream regions of atmospheric modification.

Regions where significance exceeds 95%, as determined by a Student’s t-test,

are thatched. The wind farm is located within the rectangular box over the central

United States.

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[Figure 2] Growth and propagation of

anomalies. a, A Hovmoller plot shows

the standard deviation of anomalies

versus forecast lead time and longitude,

highlighting the growth rate and group

velocity of perturbations. b, The

standard deviation over all cases of the

anomalous lower tropospheric zonal

wind field one half day after the

roughness change is depicted. This plot

is equivalent to a time slice of a at time

Day=0.5. The largest effects are

confined to the wind farm. c, Same as b

except at time Day=6.5. The largest

effects are now located over the North

Atlantic.

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[Figure 3] EOF analysis of day 5 992 millibar zonal wind. The first two

components of an EOF analysis are displayed. They depict the two largest

modes of variability associated with the surface roughness perturbation.

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[Figure 4] Mid level cloud cover. These plots of mid level cloud cover depict a

particular case where a large modification of weather occurred four days after the

surface roughness modification. a, The anomaly field (calculated as the

difference between the case with the wind farm on, and the case with it off)

shows changes in cloud cover of approximately 80%. b, The cloud field when the

wind farm was on is visibly different from c, the cloud field with the wind farm

turned off.